Cogn Process DOI 10.1007/s10339-014-0599-z
RESEARCH REPORT
Aspects of situated cognition in embodied numerosity: the case of finger counting Mirjam Wasner • Korbinian Moeller • Martin H. Fischer • Hans-Christoph Nuerk
Received: 9 June 2013 / Accepted: 3 January 2014 Marta Olivetti Belardinelli and Springer-Verlag Berlin Heidelberg 2014
Abstract Numerical cognitions such as spatial-numerical associations have been observed to be influenced by grounded, embodied and situated factors. For the case of finger counting, grounded and embodied influences have been reported. However, situated influences, e.g., that reported counting habits change with perception and action within a given situation, have not been systematically examined. To pursue the issue of situatedness of reported finger-counting habits, 458 participants were tested in three separate groups: (1) spontaneous condition: counting with both hands available, (2) perceptual condition: counting with horizontal (left-to-right) perceptual arrangement of fingers (3) perceptual and proprioceptive condition: counting with horizontal (left-to-right) perceptual arrangement of fingers and with busy dominant hand. Report of typical counting habits differed strongly between the three conditions. 28 % reported to start counting with the left hand in the spontaneous counting condition (1), 54 % in the perceptual condition (2) and 62 % in the perceptual and proprioceptive condition (3). Additionally, all participants in the spontaneous counting group showed a symmetry-based counting pattern (with the thumb as number 6), while in the two other groups, a considerable
M. Wasner (&) H.-C. Nuerk Institute of Psychology, Eberhard Karls University, Tuebingen, Schleichstr. 4, 72076 Tuebingen, Germany e-mail: [email protected] K. Moeller H.-C. Nuerk Knowledge Media Research Center, Schleichstr. 6, 72076 Tuebingen, Germany M. H. Fischer Division of Cognitive Sciences, University of Potsdam, Karl-Liebknecht-Str. 24/25, 14476 Potsdam, Germany
number of participants exhibited a spatially continuous counting pattern (with the pinkie as number 6). Taken together, the study shows that reported finger-counting habits depend on the perceptual and proprioceptive situation and thus are strongly influenced by situated cognition. We suggest that this account reconciles apparently contradictory previous findings of different counting preferences regarding the starting hand in different examination situations. Keywords Finger counting Situated cognition Number processing Finger-digit mapping
Introduction The idea of abstract cognitive representations being grounded in senso-motoric experiences has gained considerable research interest in recent years (i.e., grounded, embodied and situated cognition, e.g., Barsalou 2008; Wilson 2002; Fischer and Brugger 2011; Fischer 2012). According to this view, all or at least some of our knowledge representations remain associated with the sensory and motor features that were presented during knowledge acquisition. For the case of numerical cognition, an example for embodied cognition is finger counting (Wilson 2002; Domahs et al. 2010; Fischer and Brugger 2011; Moeller et al. 2012). Finger counting is a natural embodied expression of numerical quantities by body parts and is considered to benefit children’s learning of basic numerical and arithmetic principles (e.g., Conant 1896; Butterworth 1999; Moeller et al. 2011). A specific finger-digit representation, reflecting the way numbers are associated with specific fingers, is considered as an important moderator for mental representations and the processing of numbers
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(e.g., Fayol et al. 1998; Noe¨l 2005; Gracia-Bafalluy and Noe¨l 2008). Numerical cognitions have been observed to be influenced by grounded, embodied and situated factors (cf. Fischer and Brugger 2011; Fischer 2012). For spatialnumerical associations (SNAs), there seems to be considerable influence of grounded, embodied and situated factors (Fischer and Brugger 2011), however, for finger counting only the impact of grounded and embodied cognition has so far been studied. To our knowledge, there is no published study investigating the situated influence on the representation of finger counting. The model of grounded, embodied and situated cognition The model of Fischer and Brugger (2011) and Fischer (2012) deals with grounded, embodied and situated magnitude/numerical processing. It proposes a hierarchical relationship with these principles: The most fundamental aspect of these cognitive representations is the grounded cognition that reflects universal properties of the world, e.g., the physical principle that larger numerosities are considered as ‘‘more’’ and include smaller numerosities, unless a cognitive process intervenes. Building on grounded cognition is embodied cognition that describes the sensorimotor (embodied) knowledge representations acquired by an individual. This knowledge representation is related to culture and reflects typical learning experiences (e.g., reading direction). From our prediction, cultural differences in finger counting or in SNAs are an expression of embodied cognition. Situated cognition finally describes the flexibility of number concepts and is dependent on task-specific constraints and the current context. An example for the influence of situated factors on numerical cognition can be found in the study from Loetscher et al. (2008): Adults generated significantly more smaller random numbers in a random number generation task when they turned their head to the left and significantly fewer smaller numbers when they turned their head to the right. The model applied to spatial-numerical associations (SNAs) Above model has been successfully applied to the domain of SNA research, for which grounded, embodied and situated factors have been studied. The influence of grounded cognition can be found in results that vertical SNAs are more robust and harder to abolish than horizontal SNAs (Fischer 2012; Shaki and Fischer 2012). These findings suggest that there seems to be a universal association between smaller numbers and lower space and between larger numbers and upper space.
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Evidence for embodied factors comes from cultural differences, which have been learnt and experienced and exert differential influences for different cultures: The SNARC effect (spatial-numerical association of response codes; Dehaene et al. 1993) that describes the phenomenon that small numbers are typically associated with the left side of space, whereas large number are associated with the right side (e.g., Dehaene et al. 2003; Nuerk et al. 2005) differs reliably between cultures (Zebian 2005; Shaki and Fischer 2008; Shaki et al. 2009). For instance, Shaki et al. (2009) showed that small numbers are associated with the left in left-to-right reading culture (Canada) but associated with the right in right-to-left-reading culture (Palestine) and that the association is less consistent in a language where words are read from the right and numbers from the left (Hebrew). This is a prime example of embodied cognition, because there is neither a difference in grounded cognition, which is the same for all cultures, nor in situated cognition, because the testing situation was exactly the same for all cultures. Therefore, we would propose that these influences reflect culturally typical sensori-motor learning experiences. Interestingly, such embodied effects are not restricted to adults. Recent studies do not only indicate the presence of SNARC in preschoolers (Opfer and Furlong 2011; Patro and Haman 2012) but they also suggest that preschoolers’ SNAs are also culturally influenced (Shaki et al. 2012). It is hypothesized that observational learning and imitation of directional counting habits in adults are sources for the observed SNA bias (e.g., Shaki et al. 2012; for review see Fischer and Brugger 2011). Finally, visual-perceptive influences of situated cognition on SNAs where for instance shown by Fischer et al. (2009): Presenting either a Russian (left-to-right) or a Hebrew (right-to-left) word randomly from trial to trial influenced the bilingual participants in their SNARC effect. The SNARC effect in these participants was only present when they read the Russian left-to-right word. There are also other findings that show visual perception influences of situated cognition on the SNARC effect: Ba¨chtold et al. (1998) replicated the SNARC effect when participants thought of visually presented numbers as being arranged on a ruler (number line) but found a reversed SNARC effect when numbers were thought of as being on a clock face (where small numbers are on the right side and larger numbers on the left). However, influences are not restricted to visual perception alone. Wood et al. (2006) had participants crossed their hands and manipulated motor execution and proprioception of body parts. In the crossed hand condition, Wood et al. (2006) could not replicate the SNARC effect (but see Dehaene et al. 1993, for diverging results). Wood et al. (2006) postulated two reference frames for the SNARC effect, one related to proprioception and representation of body parts (hands) and another one to
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representational space. Similarly, motor influences on the SNARC were observed by Riello and Rusconi (2011), who observed that hand posture (palm-up or palm-down) modulates the SNARC effect. In sum, the full model of Fischer and Brugger (2011) can be applied to SNAs as grounded, embodied and situated influences on SNAs have been observed. For situated SNAs, some influences seem to be rather perceptual, while in other paradigms situated manipulation of motoric effectors (hands) influenced SNAs. The model applied to Finger counting While the full model by Fischer and Brugger (2011) has been applied to SNAs, this is not the case for finger counting. For finger counting, the influence of grounded and embodied cognition has been shown but not the influence of situated cognition. We first summarize some results for grounded and embodied cognition before we address the issue of influences from situated cognition. From a grounded cognition perspective more fingers represent a larger number and encompass larger numerosities. This is in line with the results of Di Luca et al. (2010) who could show that in a priming task canonical (i.e., countingrelated), finger postures automatically activate a placecoding representation that includes larger and smaller magnitudes as a function of prime-target distance, whereas non-canonical finger configurations activate a summation coding representation that only includes smaller magnitudes. The influence of embodied cognition can be found in cultural differences in finger-counting habits: Although finger counting can be observed in all cultures (Ifrah 1981), there is no universal finger-counting system so cultural influences seem to prevail the development on finger counting (Pika et al. 2009). Lindemann et al. (2011) observed that in comparison with finger-counting habits of participants from Western countries and the Middle East, two-thirds of the Western participants started counting with their left thumb, whereas two-thirds of the Middle Eastern participants started counting with their right pinkie. Situational influences on finger-counting preferences have, in contrast to the findings from the SNARC effect, (at least to our knowledge) not been systematically examined so far. Therefore, the first goal of the study is to examine whether the model of Fischer and Brugger (2011) can be fully applied to finger-counting preferences as it has been applied to SNAs. Despite this theoretical model testing, such situated influences may also be important to reconcile apparently inconsistent findings regarding counting preferences in European participants. The studies that have been conducted so far revealed inconsistent results, in particular so with respect to the hand with which participants started
counting and the transition to the second hand when counting numbers larger than 5 (Di Luca et al. 2006; Fischer 2008; Sato and Lalain 2008; Lindemann et al. 2011; review in Previtali et al. 2011). While Previtali et al. (2011) suggest that these different results mainly derive from handedness preferences and discuss the plausibility of multiple and coexistent number–space mappings, we suggest that the inconsistent results regarding finger-counting preferences may have their origin in influences of situated cognition. The inconsistent results regarding counting preferences are reviewed hereafter with special regard to situational differences. How finger-counting habits vary: hand-based effects The study by Sato and Lalain (2008) examined the hand-digit mapping in French children and adults and found that 69 % of them started counting with their right hand. These results were relatively stable across the age groups studied. Corroborating the notion of predominantly right-hand starting, Di Luca et al. (2006) showed that Italian participants performed significantly better in a number discrimination task when using the ‘‘prototypical Italian finger-counting mapping’’ (that was to start with the right hand to count from 1 to 5 and then switch to the left hand to count on from 6 to 10, cf. Di Luca et al. 2006, p. 1658), in comparison with other mappings such as starting to count with the left hand. Moreover, Sato et al. (2007) found a neural link between numbers and fingers in adults, especially between the right hand and small numbers. In their study, participants had to perform a parity judgment task. Results showed a specific increase in corticospinal excitability of right-hand muscles when relatively small numbers (1–4) were presented (see also Andres et al. 2007, for similar findings). In contrast, in the study of Fischer (2008) results from a questionnaire study showed that two-thirds of the 445 Scottish participants started finger counting with their left hand regardless of their handedness. These reports were substantiated by results from Lindemann et al. (2011) who observed in a cultural comparison study that two-thirds of the Western participants started counting with their left thumb, using an internet-based version of the same as Fischer (2008). Interestingly, apart from inconsistencies with respect to the starting hand, there are further differences between published reports on the finger level, in particular regarding which finger corresponds to the number 6. These will be reviewed next. How finger counting varies: finger-based effects Sato and Lalain (2008) reported that all but three of their participants (all in the age group 4–5 years old, total
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n = 117) showed a symmetry-based finger-digit mapping with the thumb as finger number 6 (symmetrically to the other thumb as number one). In contrast, the study of Lindemann et al. (2011) found that about 32 % of their Western participants continued counting to number six with the pinkie of their right or left hand instead of the thumb. The observation of Lindemann et al. (2011) is inconsistent with the thumb representing the general starting point of the counting procedure independent of starting or transition hand. It does, however, reflect a spatial continuity in the finger-counting process, assuming both hands are held with their palms up with the pinkies of the left and right hand next to each other.
Ad (2) the influence of proprioception: it seems plausible that participants completed the questionnaire by using their dominant hand to write or click (paper–pencil questionnaire or online study), which was the right hand in the majority of cases. In turn, this may have led to a more frequent use of the freely available left hand when starting to count, despite the explicit instruction to hold both empty hands up when counting in the studies of Fischer (2008) and Lindemann et al. (2011). If we apply above model of Fischer and Brugger (2011) to the case of finger counting, such situated cognition factors (here visual perception and proprioception) should influence the embodied cognition on finger counting.
What are possible situated cognition factors in finger-counting assessment?
The current study
Following above idea of situated cognition—as a possible influencing factor of the characteristics of the assessment of finger counting on observed finger-counting habits—a closer inspection of the assessment procedures employed in recent studies may be informative. Indeed, there are significant differences in the assessment of finger-counting habits between those studies. The study of Sato and Lalain (2008) had a more natural setting, where participants were asked to count spontaneously from one to ten with their fingers and were observed while doing so. Consequently they counted freely and no obvious influencing situated factor was present while doing so. Instead, the results of Fischer (2008) and Lindemann et al. (2011) were mainly based on questionnaire data. With having the questionnaire data, there were two main factors that might be situated influencing factors: (1) visual perception, e.g., reading text and visual input from the instruction (e.g., left-to-right arrangement of fingers in the questionnaire) and (2) proprioception that can be described as the sense of the body and its parts, i.e., for our study, the sense for postures and locations. Ad (1) the visual perception: In the questionnaire-studies (Fischer 2008; Lindemann et al. 2011), the instruction was to ‘‘hold your empty hands in front of you and then count aloud from one to ten, using your fingers as you count’’. (see Lindemann et al. 2011). In line with the data reported by Riello and Rusconi (2011), one may argue that, due to the horizontal (left-to-right) perceptual arrangement of fingers of the displayed hands being held palms up (see Fig. 1 Panel b), counting more frequently started on the hand for which mental number line direction and fingercounting sequence matched (i.e., the left hand). Additionally, participants had to read the instruction prior to filling out the questionnaire, so that a left-to-right scheme might have been pre-activated even before participants started to count on their fingers (cf. Shaki and Fischer 2008).
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Based on above model assumption, the aim of the current study was straightforward. We wanted to explore the impact of situated cognition on finger counting by systematically manipulating influence of (1) visual perception (visual input through the horizontal (left-to-right) perceptual arrangement of displayed fingers and instruction) and the influence of (2) proprioception (e.g., writing with a pen before counting) in three different conditions: For a first group of participants, there was no or little situated influence. Participants were just asked to count spontaneously with their fingers, with the finger-counting sequence being watched and noted by the experimenter (corresponding to Sato and Lalain 2008). The second group had only visual perception influence by giving the instruction from the questionnaire orally but with having a horizontal (left-toright) perceptual arrangement of fingers. The instruction for this group was given orally to avoid possible influences of proprioception. For the third group, comparable to Fischer (2008), we synced influence of visual perception and proprioception by using a written instruction in a questionnaire, in which participants had to write down their finger-counting sequence. Prior to the counting, they had to use their dominant hand to fill in the questionnaire. We expected that of those participants who were just asked to count spontaneously and had no intentional influence from situated cognition, most should start counting with their (dominant) right hand (as in Sato and Lalain 2008). In the intermediate group with having just one influencing situated factor (visual perception), we hypothesized that they are less likely to start counting with their (dominant) right hand because of the horizontal (leftto-right) perceptual arrangement of fingers. It is assumed that this left-to-right arrangement leads to the report of more left-starters than in the spontaneous counting group. Further, we expected that participants who had situated influence from (1) proprioception (e.g., writing with a pen prior to counting) and (2) visual perception (e.g., instruction
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a
b
Fig. 1 Experimental setting and instruction in the three participant groups. a Depicts the three participant groups (spontaneous counting condition, perceptual condition, perceptual and proprioception
condition). b Shows the instruction of the questionnaire from group 3 that got the instruction in a written way and used their dominant hand prior to the counting
and displayed hands) should start counting mostly with their left hand (comparable to Fischer 2008). In this case, there is not only influence from the horizontal (left-to-
right) perceptual arrangement of fingers but also the use of the dominant hand prior to counting that is assumed to have a further influence on the report of finger counting. For left-
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starters, we hypothesized that there are the fewest in the first spontaneous counting group but more in the second group with influence from visual perception and most in the group with influences from visual perception and proprioception. Regarding the transition to the second hand (from 5 to 6), we expect that groups also differ in their shown preferences to continue counting with the second hand. Corresponding to Sato and Lalain (2008), we expected that almost all of participants from the spontaneous counting group should proceed with their thumb. Having activated a left-to-rightscheme, we hypothesized that in the group of participants that experienced influence from visual perception more participants should continue counting with their pinkie compared to the spontaneous counting group. In the group with influence from visual perception and proprioception, we expected that similar to Lindemann et al. (2011) that a certain amount of people, more than in the other two conditions, should do the transition to the second hand with using their pinkie.
Methods Participants 458 German participants (237 female, 52 %) took part in the study. Mean age for all groups was 24.70 years (SD = 8.99 years; range: 16.08–79.25 years). Differentiated by each group, mean age was 37.84 (SD = 16.74) years for the spontaneous counting group, 23.73 years (SD = 3.12 years) for the second group with influence from visual perception and 24.27 years (SD = 3.98 years) for the third group with influence from visual perception and proprioception. Age differed significantly between groups (F (2) = 108.40, p \ .001). Participants were either undergraduate students or random passersby that were naı¨ve to the intention of the study. The random passersby were chosen because we wished to examine natural spontaneous counting habits of naı¨ve participants in a situation as natural as possible (i.e., not in an experimental room of the psychological department). For the other conditions, in which situated cognition was manipulated anyway by perceptual or proprioceptive factors, the situation in which counting habits were assessed, was not natural anyway, therefore, these conditions were administered at university. For this reason, random passersby from the spontaneous counting group were standing, while participants from the other two groups were sitting. The majority of participants (95 %) of had Abitur, a general qualification for university.
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Procedure We assigned participants to three groups by means of the experimental setting given: the two questionnaire groups with situated influencing factors were tested in different university courses, whereas for the spontaneous counting group random pedestrians were asked to participate. For a detailed description of groups, see Fig. 1 Panel a. The spontaneous counting group was asked to count spontaneously. Participants had to have both hands freely available and were then asked to count to ten with their fingers. Finger-counting habits were watched and noted by the experimenter (see Fig. 1 Panel a, top chart). The instruction differed slightly from that of the questionnaire conditions by saying: ‘‘Could you please count with your fingers from 1 to 10’’. Prior to the finger-counting assessment, participants performed some finger-hand pantomime activities to assess their handedness (spreading butter, dealing cards, lighting a match). Due to these pantomime activities, participants activated both hands prior to counting and not just mainly one hand (like in the proprioceptive condition, where participants had written with one hand before). After activating both hands, it was assured that participants had both hands freely available, so that there was no proprioceptive bias for natural counting. In the second group with influence from visual perception (see Fig. 1 Panel a, central chart), the instruction was: ‘‘Please hold your empty hands in front of you and then count aloud from one to five, using your fingers as you count’’. Influence of visual perception was due to the spatial left-to-right arrangement of fingers in the questionnaire (see Fig. 1 Panel a, central chart). This instruction was given orally, so that they had both hands available prior to the counting and no influence from proprioception. Participants were asked to count to ten with their fingers and then fill in the finger counting as well as demographic and handedness questionnaire after counting was completed. In line with the procedure of previous studies (Fischer 2008; Lindemann et al. 2011), the third group with influences from visual perception and proprioception received a written instruction with a customized print-out version of the online questionnaire from Lindemann et al. (2011), (see http://fingercounting.cognitive-psychology.eu/hcq_ paper_supplementary/). Prior to the finger-counting task (see Fig. 1, Panel a, lower chart), a demographic and handedness questionnaire had to be completed. This means that they used their dominant hand prior to finger counting (influence of proprioception) and were influenced by the spatial arrangement of fingers. The hand posture in this group was predefined by the form of instruction: palm-up, next to each other.
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Of the 458 included participants, 68 (50 % female, 93 % right-handed) were asked to count spontaneously, 252 (44 % female, 90 % right-handed) were in the second group with influence from visual perception and 138 (68 % female, 90 % right-handed) were in the third group with influence from visual perception and proprioception. Handedness About 91 % of the sample was right-handed (n = 415), 7 %, left-handed (n = 29) and 3 %, bilateral (n = 14). Of these 29 left-handers, 24 (83 %) started counting with their dominant hand, whereas there was no such tendency in right-handers for whom starting hand was balanced (50 % right-starters). In the spontaneous counting group, three activities were monitored as participants were instructed to pantomime them prior to the counting: (1) to hand out playing cards, (2) to spread butter on bread and (3) to light a match. Additionally, participants were asked about their handedness to confirm the handedness-activity judgment. In the two groups with influence from situated cognition, handedness was assessed with 13 items (e.g., Which hand do you use for… writing?), similar to the study by Fischer (2008).
Results When there were directed empirical hypotheses, these hypotheses were statistically tested in a directed way (e.g., one sided) whether possible to match empirical and statistical hypotheses as closely as possible, because overall statistics can be too conservative and thus misleading (e.g., Hager 2002). All but one participant used the fingers of both hands to count from one to ten; so, they started with either their left or right hand for the first five numbers and continued counting with the other hand for numbers six to ten. The person who counted with only one hand used the right hand and was in the third group with influence from visual perception and proprioception. Hand-based results Results showed that participant groups differed systematically with respect to the hand with that counting was started [v2(2) = 21.89, p \ .001]. When participants counted spontaneously with no influence of situated cognition, only about 28 % started with their left hand. In the second group with influence from visual perception, preference was approximately balanced with 54 % left-starters. Contrarily, in the third group with influences from visual
Fig. 2 Percentage distribution of right- and left-starters in the three different instruction conditions. Note that in the spontaneous counting group most participants started with their right hand, whereas the more situated influences the more participants started with their left hand
perception and proprioception, about 62 % started counting with their left hand (see Fig. 2). More specific testing revealed that the reversal from 72 % right-starters in the spontaneous counting group to 62 % leftstarters in the group with influences from visual perception and proprioception was significant [v2(1) = 21.54, p \ .001]. Additionally, the shift from 28 % left-starters in the spontaneous counting group to 54 % left-starters in second group with influences from visual perception was significant [v2(1) = 14.09, p \ .001]. Finally, the difference between the two groups that were influenced by situated cognition was also significant [v2(1) = 2.78, p \ .05]. Finger-based results Almost all participants (98 %) started counting with either one of their thumbs. However, the transition to the second hand (finger number 6) differed significantly between groups [v2(6) = 46.75, p \ .001]. As illustrated in Fig. 3, all participants (100 %) in the spontaneous counting group with both hands available continued counting on their second hand with their right/left thumb. In the group with influence from visual perception, 13 % continued with their right pinkie (6 % left pinkie), and 26 % of the participants that were influenced by visual perception and proprioception continued with their right pinkie (4 % left pinkie). Additional testing indicated that the finger used to count number six differed significantly for all pairwise comparisons between the three instruction groups [all v2(3) [ 10.80, all p \ .013]. Possible gender differences There were unexpected gender differences between the instruction groups. In the spontaneous counting group with
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Fig. 3 Percentage distribution of fingers corresponding to the number six separated for the three different instruction conditions. Note that no one in the spontaneous counting group continued with their pinkie, whereas in the other two questionnaire groups with influence of situated factors a considerable part (20–30 %) of the participants did. This pattern is related to a spatial congruent counting pattern. Again this pattern was most pronounced in the group with visual perception and proprioception
both hands freely available (50 % female participants), no gender differences were found. Differences between male and female participants were observed in second group with influences from visual perception (44 % female participants) with respect to the finger associated with number six. This was mainly because women continued counting with their right pinkie about as often as with their left pinkie (10 %, respectively, 11 %), whereas men tended to count on more likely with their right pinkie (15 %) and only rarely with their left pinkie (2 %) when they continued with their pinkie. In the third group with influences from visual perception and proprioception (68 % female participants), differences were observed for the finger associated with number one and number six. Results showed that women were particularly more likely to start with their left hand in the instruction group, whereas starting hand was almost balanced in men.
Discussion Finger-counting habits are influenced by situated cognition: Hand-based effects Based on the model of Fischer and Brugger (2011; see also Fischer 2012), we hypothesized that besides grounded and embodied aspects, finger-counting habits are also influenced by situated aspects. Therefore, we assessed the finger-counting patterns of three different groups and varied the amount of situated influences: (1) spontaneous counting with both hands available (as in Sato and Lalain 2008), (2) visual perception: counting with horizontal (left-to-right) perceptual arrangement of fingers (3) visual perception and proprioception:
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counting with horizontal (left-to-right) perceptual arrangement of fingers and with busy dominant hand prior to counting (as in Fischer 2008). Participants in the spontaneous counting group had no or just little influence of situated cognition as the setting was natural and the instruction did not pre-activate a specific spatial representation. Congruent to other studies, we expected most participants to start with the (dominant) right hand (Di Luca et al. 2006; Sato and Lalain 2008). In the perceptual condition, participants were tested with a questionnaire that showed a horizontal left-to-right arrangement of fingers. We hypothesized that due to the visual perception of the finger arrangement, participants should count differently compared to spontaneous counting with more left-starters because of the given horizontal (left-to-right) arrangement in the German left-to-right reading culture. In the perceptual and proprioceptive condition, participants not only were influenced by the horizontal (left-to-right) perceptual arrangement of fingers but also used their dominant (right) hand for writing and holding a pen prior to the counting (proprioception). Therefore, there were two situated factors that—according to our extension of the Fischer and Brugger (2011) model— should influence participants even stronger than the group with only visual perception; so, we expected that the majority would be left-starters similar as it was in Fischer (2008) and Lindemann et al. (2011). In line with these hypotheses, the current results indicate that finger-counting patterns indeed differed depending on situational factors at the time of data collection. Depending on condition, we observed reliable differences between participant groups regarding the starting hand (right or left): In the spontaneous counting group with no or little influence of situated factors, only 28 % of participants were left-starters. In the second condition, in which visual perception (left-to-right alignment of hands/finger) was present, significantly more participants started with the left hand (54 %). Finally, in the group with perceptual and proprioceptive influences, even more participants (62 %) started to count with their left hand. These data show that the proportion of left- and right-starters almost reversed (72 % right-starters in condition 1, but 62 % left-starters in condition 3) and thus showed a pronounced impact of the situational manipulation. In our view, this is strong evidence that not only grounded factors based on universal physical laws of the world, and embodied factors, based on culturally mediated sensori-motor learning directions (e.g., reading direction), but also situated factors strongly influences participants’ report of their finger-counting habits. The situated cognition account reconciles apparently inconsistent findings in the literature Such a situated cognition account of finger-counting habits is not only theoretically interesting for the validity of the
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Fischer and Brugger (2011) model for finger counting. Rather, this account has also important practical implication because it reconciles apparently inconsistent results in the literature: For our questionnaire instruction groups with influences from situated factors, we used the same questionnaire as Fischer (2008) and Lindemann et al. (2011) and observed congruent results with about two-thirds of participants being left-starters. In contrast, in the spontaneous counting group with both hands freely available, we replicated the experimental setting of Sato and Lalain (2008) and obtained similar results with about three quarters of participants starting with their right hand. Thus, we can assume that the stronger situational influences of perceptual or proprioceptive aspects favoring a left hand start of finger counting in a left-to-right reading culture, the greater is the proportion of left-starters. In the group with two influencing situated factors, most participants started with their left hand, in the group with one influencing factor about half of the participants started with their left hand and in the spontaneous counting group with no or only little situated influence an minority started with the left hand. While our study provides evidence that the examination situation influences responses, we also wish to acknowledge that there may be other situated factors, which may influence responses differentially in different experiments and may contribute to of finger-counting habits being modulated by situational factors. For instance, we tried to realize a natural setting in the spontaneous counting group similar to Sato and Lalain (2008) and examined participants even outside formal experimental laboratories to obtain a finger-counting report as natural and as naı¨ve as possible. On the other hand, we used questionnaire conditions as in Fischer (2008) or Lindemann et al. (2011) for which people have to fill out a questionnaire form prior to counting. Despite the visual-perceptive and proprioceptive manipulations we examined, these led to some other situated influences regarding experimental group (students vs. random passersby) and differences in body position (sitting vs. standing) in the spontaneous counting versus the other two groups. Additionally, it is conceivable that even within the spontaneous counting group who had both hands freely available and activated before counting, spontaneous hand or finger postures (e.g., palm-up, palm-down, cf. Riello and Rusconi 2011) prior to counting may also lead to situated influences, which influence counting habits. The demonstration of some situated cognition aspects strongly influencing finger counting does not preclude that other associated or not manipulated situated aspects can also influence finger-counting habits in this and other studies. Given that the situated manipulations revealed rather large effects in our study, further investigation of situated fingercounting factors seems worthwhile in our view.
Finger-counting habits are influenced by situated cognition: finger-based effects Further evidence that situated cognition had an important influence on the number-to-finger mapping came from the results regarding the finger associated with the number six. All participants in the spontaneous counting group continued counting with their thumb when transferring from 5 to 6. This was different in the other two conditions: About 20 % (perceptual condition) and 30 % (perceptual and proprioceptive condition), respectively, used their pinkie to indicate finger number six. So, one can assume that situated factors led to a specific hand position that activated a spatially continuous representation in 20–30 % of the participants in the questionnaire instruction groups with influencing situated factors. This pattern was again significantly stronger for influences from perception and proprioception compared to the influence of perception only. According to our theoretical account that the situated influence triggered a left-to-right-scheme, most of the participants with a spatially continuous pattern counted in a way replicating a left-to-right oriented number line where—when looking at hands palm-up—there is a continuous transition from the left to the right pinkie. We assume that the situated influence from the horizontal (leftto-right) perceptual arrangement of fingers as well as the prior use of the dominant (right) hand corroborated the activation of such a mental number line representation from left-to-right. This is in line with the results of Riello and Rusconi (2011) who found that a palm-up posture of the left hand facilitates a systematic left-to-right oriented mental number line representation. An extension and specification of the Fischer and Brugger (2011) model to finger-counting habits Generally, these results fit to the model of grounded, embodied and situated cognition (Fischer and Brugger 2011; Fischer 2012). According to the model grounded cognition can be described as universal features that apply to physical laws, e.g., that larger numerosities are more and include smaller numerosities. Embodied cognition is defined as sensori-motor (embodied) knowledge representation that is acquired during typical learning and is formed by culture, while situated cognition can be seen as the influence of situation and context that affects different results due to different situations a person is examined in. Within SNAs, grounded, embodied and situated cognition seem to be well established as described in the introduction. These results for SNAs will be shortly summarized here before generalizing these results to finger counting: (1) The influence of grounded cognition can be found in results that show the universal association
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between smaller numbers and lower space, respectively, between larger numbers and upper space (Fischer 2012; Shaki and Fischer 2012). (2) Influence on embodied cognition can be found in the study from Shaki et al. (2009) that show that different cultures differ in the direction of the SNARC effect. (3) Influences of situated cognition on SNAs can be found in different studies, e.g., Fischer et al. (2009): Bilingual participants saw randomly from trial to trial either a Russian (left-to-right) or a Hebrew (right-toleft) word. The SNARC effect in these participants was only present when they read the Russian left-to-right word. We adapted this model from Fischer and Brugger (2011) and Fischer (2012) to specifically incorporate finger counting (see Fig. 4). When looking at finger-counting habits, studies regarding grounded and embodied cognition only have been reported so far (e.g., Di Luca et al. 2010; Lindemann et al. 2011, see introduction). Within finger counting, grounded cognition means that a larger numerosity of fingers represent a larger number and (at least for the Western counting system) includes smaller numerosities. This is in line with the results of Di Luca et al. (2010) regarding place versus summation coding in a priming task. Cultural differences measured with the same questionnaire indicate influences of embodied cognition (Lindemann et al. 2011). However, from our point of view, there was a gap regarding the influence of situated cognition in finger counting. With the present study, we tried to close this gap by showing the influence of situated cognition on natural finger-counting habits. In the present study, these situational factors can be described as visual perception and proprioception (see Fig. 4). From the current results, we conclude that there are
Situated cognition Influence of testing-situation e.g., left-to-right arrangement of fingers and one hand busy holding pencil visual perception
Present study
proprioception
Embodied cognition Typical body postures/ typical spatial reference frame related to culture or typical learning (e.g., reading direction)
Grounded cognition Larger numerosities are more e.g., more fingers represent larger numbers
e.g., Lindemann et al. (2011)
e.g., Di Luca et al. (2010)
Fig. 4 Extension and specification of the Fischer and Brugger (2011) model to finger-counting habits. Influences of grounded, embodied and situated cognition on finger counting are displayed. The present study examines influencing factors from situated cognition
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indeed influences of situated factors that modulate participants finger-counting habits (even within the same culture). Interestingly, the results of our study show not only an influence of situated cognition but results also indicate that the power of this situated influence can be varied. The more influencing situated factors favored left-to-right counting habits the more participants tended to be leftstarters: From 28 % left-starters in the spontaneous condition, proportion of left-starters rose to 54 % with one influencing situational component favoring left-starting in our culture (visual perception of the left-to-right arrangement of fingers) and further on to 62 % with two components of situated influence (visual perception and proprioception). In the finger-counting model (see Fig. 4), this aspect is indicated by different pathways from situated to embodied cognition. Note that these pathways also indicate that the influence of situated factors may differ depending on the embodied representation it addresses. For instance, in right-to-left-reading cultures horizontal alignment of fingers may activate right-to-left SNAs (e.g., Shaki et al. 2009) and therefore lead to more right-hand starters rather than to more left-starters as in the current study.
Conclusions and perspectives Based on the present data and their theoretical implementation, we suggest that finger counting (in Western cultures) is stereotypical in certain ways, as participants almost always started with either one of their thumbs. However, the use of the right or left hand seems to be highly susceptible to the influence of situated factors. When people count on their fingers spontaneously and have both hands available, they seem to prefer to start finger counting with their dominant (right) hand. This result is in line with Previtali et al. (2011) who suggest that starting hand preference mainly derive from handedness preferences. Visual perception of a left-to-right arrangement of fingers and the proprioception of holding a pen in the dominant (right) hand prior to counting might increased the influence of a mental left-to-right-scheme, so that increasingly more participants started to count with their left hand. Extending the notion of the embodiment of cognitive processes, in which the spontaneous typical finger-counting habit is seen as an instance of embodied cognition (Domahs et al. 2010; Fischer and Brugger 2011; see Barsalou 2008 and Wilson 2002 for an overview of embodied cognition), we argue that counting patterns are influenced by situated cognition. This is in line with the idea of situated cognition to depend on task-relevant inputs and outputs (Wilson 2002; Robbins and Aydede 2009). A tentative explanation for the observed gender differences might be that different spatial schemes are activated
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in men or women due to the influence of visual perception and proprioception. One might suspect that women are more influenced by the spatial orientation of their hands. The influence of situated cognition could have lead to a faster activation of the left-to-right-scheme, so that therefore women are more likely left-starters. However, at this point this remains speculative and needs to be investigated systematically in future studies evaluating what underlying processes may contribute to the observed differences in counting patterns between men and women. Taken together, we argue that finger counting is influenced by grounded, embodied and situated cognition (see Fig. 4). In this study, we examined the influence of situated cognition, in particular, visual perception and proprioception. By simply manipulating the amount of situated cognition, we could observe significant differences in counting patterns within the same culture. We conclude that when counting spontaneously, handedness preference determines starting hand, but when left-to-right schemes are pre-activated due to situated factors a shift to increasingly more left-starters and a more spatial congruent transition to the second hand can be observed. This corroborates the relevance of situated cognition because even a highly overlearnt practice such as finger counting depends strongly on its situational constraints. We suggest that the situational constraints in our study as well as other possible situational aspects should be further studied to obtain a better picture on the situated cognition influences on finger counting. Acknowledgments Mirjam Wasner, Korbinian Moeller and HansChristoph Nuerk are members of the ‘‘Cooperative Research Training Group’’ of the University of Education, Ludwigsburg and the University of Tuebingen, which is supported by the Ministry of Science, Research and the Arts in Baden-Wu¨rttemberg. They are also associated with the LEAD Graduate School of the University of Tuebingen, which is funded within the framework of the Excellence Initiative via the German Research Foundation. Martin H. Fischer was supported through DFG Grant FI 1915/2-1 on ‘‘Manumerical cognition’’.
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RESEARCH REPORT
Aspects of situated cognition in embodied numerosity: the case of finger counting Mirjam Wasner • Korbinian Moeller • Martin H. Fischer • Hans-Christoph Nuerk
Received: 9 June 2013 / Accepted: 3 January 2014 Marta Olivetti Belardinelli and Springer-Verlag Berlin Heidelberg 2014
Abstract Numerical cognitions such as spatial-numerical associations have been observed to be influenced by grounded, embodied and situated factors. For the case of finger counting, grounded and embodied influences have been reported. However, situated influences, e.g., that reported counting habits change with perception and action within a given situation, have not been systematically examined. To pursue the issue of situatedness of reported finger-counting habits, 458 participants were tested in three separate groups: (1) spontaneous condition: counting with both hands available, (2) perceptual condition: counting with horizontal (left-to-right) perceptual arrangement of fingers (3) perceptual and proprioceptive condition: counting with horizontal (left-to-right) perceptual arrangement of fingers and with busy dominant hand. Report of typical counting habits differed strongly between the three conditions. 28 % reported to start counting with the left hand in the spontaneous counting condition (1), 54 % in the perceptual condition (2) and 62 % in the perceptual and proprioceptive condition (3). Additionally, all participants in the spontaneous counting group showed a symmetry-based counting pattern (with the thumb as number 6), while in the two other groups, a considerable
M. Wasner (&) H.-C. Nuerk Institute of Psychology, Eberhard Karls University, Tuebingen, Schleichstr. 4, 72076 Tuebingen, Germany e-mail: [email protected] K. Moeller H.-C. Nuerk Knowledge Media Research Center, Schleichstr. 6, 72076 Tuebingen, Germany M. H. Fischer Division of Cognitive Sciences, University of Potsdam, Karl-Liebknecht-Str. 24/25, 14476 Potsdam, Germany
number of participants exhibited a spatially continuous counting pattern (with the pinkie as number 6). Taken together, the study shows that reported finger-counting habits depend on the perceptual and proprioceptive situation and thus are strongly influenced by situated cognition. We suggest that this account reconciles apparently contradictory previous findings of different counting preferences regarding the starting hand in different examination situations. Keywords Finger counting Situated cognition Number processing Finger-digit mapping
Introduction The idea of abstract cognitive representations being grounded in senso-motoric experiences has gained considerable research interest in recent years (i.e., grounded, embodied and situated cognition, e.g., Barsalou 2008; Wilson 2002; Fischer and Brugger 2011; Fischer 2012). According to this view, all or at least some of our knowledge representations remain associated with the sensory and motor features that were presented during knowledge acquisition. For the case of numerical cognition, an example for embodied cognition is finger counting (Wilson 2002; Domahs et al. 2010; Fischer and Brugger 2011; Moeller et al. 2012). Finger counting is a natural embodied expression of numerical quantities by body parts and is considered to benefit children’s learning of basic numerical and arithmetic principles (e.g., Conant 1896; Butterworth 1999; Moeller et al. 2011). A specific finger-digit representation, reflecting the way numbers are associated with specific fingers, is considered as an important moderator for mental representations and the processing of numbers
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(e.g., Fayol et al. 1998; Noe¨l 2005; Gracia-Bafalluy and Noe¨l 2008). Numerical cognitions have been observed to be influenced by grounded, embodied and situated factors (cf. Fischer and Brugger 2011; Fischer 2012). For spatialnumerical associations (SNAs), there seems to be considerable influence of grounded, embodied and situated factors (Fischer and Brugger 2011), however, for finger counting only the impact of grounded and embodied cognition has so far been studied. To our knowledge, there is no published study investigating the situated influence on the representation of finger counting. The model of grounded, embodied and situated cognition The model of Fischer and Brugger (2011) and Fischer (2012) deals with grounded, embodied and situated magnitude/numerical processing. It proposes a hierarchical relationship with these principles: The most fundamental aspect of these cognitive representations is the grounded cognition that reflects universal properties of the world, e.g., the physical principle that larger numerosities are considered as ‘‘more’’ and include smaller numerosities, unless a cognitive process intervenes. Building on grounded cognition is embodied cognition that describes the sensorimotor (embodied) knowledge representations acquired by an individual. This knowledge representation is related to culture and reflects typical learning experiences (e.g., reading direction). From our prediction, cultural differences in finger counting or in SNAs are an expression of embodied cognition. Situated cognition finally describes the flexibility of number concepts and is dependent on task-specific constraints and the current context. An example for the influence of situated factors on numerical cognition can be found in the study from Loetscher et al. (2008): Adults generated significantly more smaller random numbers in a random number generation task when they turned their head to the left and significantly fewer smaller numbers when they turned their head to the right. The model applied to spatial-numerical associations (SNAs) Above model has been successfully applied to the domain of SNA research, for which grounded, embodied and situated factors have been studied. The influence of grounded cognition can be found in results that vertical SNAs are more robust and harder to abolish than horizontal SNAs (Fischer 2012; Shaki and Fischer 2012). These findings suggest that there seems to be a universal association between smaller numbers and lower space and between larger numbers and upper space.
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Evidence for embodied factors comes from cultural differences, which have been learnt and experienced and exert differential influences for different cultures: The SNARC effect (spatial-numerical association of response codes; Dehaene et al. 1993) that describes the phenomenon that small numbers are typically associated with the left side of space, whereas large number are associated with the right side (e.g., Dehaene et al. 2003; Nuerk et al. 2005) differs reliably between cultures (Zebian 2005; Shaki and Fischer 2008; Shaki et al. 2009). For instance, Shaki et al. (2009) showed that small numbers are associated with the left in left-to-right reading culture (Canada) but associated with the right in right-to-left-reading culture (Palestine) and that the association is less consistent in a language where words are read from the right and numbers from the left (Hebrew). This is a prime example of embodied cognition, because there is neither a difference in grounded cognition, which is the same for all cultures, nor in situated cognition, because the testing situation was exactly the same for all cultures. Therefore, we would propose that these influences reflect culturally typical sensori-motor learning experiences. Interestingly, such embodied effects are not restricted to adults. Recent studies do not only indicate the presence of SNARC in preschoolers (Opfer and Furlong 2011; Patro and Haman 2012) but they also suggest that preschoolers’ SNAs are also culturally influenced (Shaki et al. 2012). It is hypothesized that observational learning and imitation of directional counting habits in adults are sources for the observed SNA bias (e.g., Shaki et al. 2012; for review see Fischer and Brugger 2011). Finally, visual-perceptive influences of situated cognition on SNAs where for instance shown by Fischer et al. (2009): Presenting either a Russian (left-to-right) or a Hebrew (right-to-left) word randomly from trial to trial influenced the bilingual participants in their SNARC effect. The SNARC effect in these participants was only present when they read the Russian left-to-right word. There are also other findings that show visual perception influences of situated cognition on the SNARC effect: Ba¨chtold et al. (1998) replicated the SNARC effect when participants thought of visually presented numbers as being arranged on a ruler (number line) but found a reversed SNARC effect when numbers were thought of as being on a clock face (where small numbers are on the right side and larger numbers on the left). However, influences are not restricted to visual perception alone. Wood et al. (2006) had participants crossed their hands and manipulated motor execution and proprioception of body parts. In the crossed hand condition, Wood et al. (2006) could not replicate the SNARC effect (but see Dehaene et al. 1993, for diverging results). Wood et al. (2006) postulated two reference frames for the SNARC effect, one related to proprioception and representation of body parts (hands) and another one to
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representational space. Similarly, motor influences on the SNARC were observed by Riello and Rusconi (2011), who observed that hand posture (palm-up or palm-down) modulates the SNARC effect. In sum, the full model of Fischer and Brugger (2011) can be applied to SNAs as grounded, embodied and situated influences on SNAs have been observed. For situated SNAs, some influences seem to be rather perceptual, while in other paradigms situated manipulation of motoric effectors (hands) influenced SNAs. The model applied to Finger counting While the full model by Fischer and Brugger (2011) has been applied to SNAs, this is not the case for finger counting. For finger counting, the influence of grounded and embodied cognition has been shown but not the influence of situated cognition. We first summarize some results for grounded and embodied cognition before we address the issue of influences from situated cognition. From a grounded cognition perspective more fingers represent a larger number and encompass larger numerosities. This is in line with the results of Di Luca et al. (2010) who could show that in a priming task canonical (i.e., countingrelated), finger postures automatically activate a placecoding representation that includes larger and smaller magnitudes as a function of prime-target distance, whereas non-canonical finger configurations activate a summation coding representation that only includes smaller magnitudes. The influence of embodied cognition can be found in cultural differences in finger-counting habits: Although finger counting can be observed in all cultures (Ifrah 1981), there is no universal finger-counting system so cultural influences seem to prevail the development on finger counting (Pika et al. 2009). Lindemann et al. (2011) observed that in comparison with finger-counting habits of participants from Western countries and the Middle East, two-thirds of the Western participants started counting with their left thumb, whereas two-thirds of the Middle Eastern participants started counting with their right pinkie. Situational influences on finger-counting preferences have, in contrast to the findings from the SNARC effect, (at least to our knowledge) not been systematically examined so far. Therefore, the first goal of the study is to examine whether the model of Fischer and Brugger (2011) can be fully applied to finger-counting preferences as it has been applied to SNAs. Despite this theoretical model testing, such situated influences may also be important to reconcile apparently inconsistent findings regarding counting preferences in European participants. The studies that have been conducted so far revealed inconsistent results, in particular so with respect to the hand with which participants started
counting and the transition to the second hand when counting numbers larger than 5 (Di Luca et al. 2006; Fischer 2008; Sato and Lalain 2008; Lindemann et al. 2011; review in Previtali et al. 2011). While Previtali et al. (2011) suggest that these different results mainly derive from handedness preferences and discuss the plausibility of multiple and coexistent number–space mappings, we suggest that the inconsistent results regarding finger-counting preferences may have their origin in influences of situated cognition. The inconsistent results regarding counting preferences are reviewed hereafter with special regard to situational differences. How finger-counting habits vary: hand-based effects The study by Sato and Lalain (2008) examined the hand-digit mapping in French children and adults and found that 69 % of them started counting with their right hand. These results were relatively stable across the age groups studied. Corroborating the notion of predominantly right-hand starting, Di Luca et al. (2006) showed that Italian participants performed significantly better in a number discrimination task when using the ‘‘prototypical Italian finger-counting mapping’’ (that was to start with the right hand to count from 1 to 5 and then switch to the left hand to count on from 6 to 10, cf. Di Luca et al. 2006, p. 1658), in comparison with other mappings such as starting to count with the left hand. Moreover, Sato et al. (2007) found a neural link between numbers and fingers in adults, especially between the right hand and small numbers. In their study, participants had to perform a parity judgment task. Results showed a specific increase in corticospinal excitability of right-hand muscles when relatively small numbers (1–4) were presented (see also Andres et al. 2007, for similar findings). In contrast, in the study of Fischer (2008) results from a questionnaire study showed that two-thirds of the 445 Scottish participants started finger counting with their left hand regardless of their handedness. These reports were substantiated by results from Lindemann et al. (2011) who observed in a cultural comparison study that two-thirds of the Western participants started counting with their left thumb, using an internet-based version of the same as Fischer (2008). Interestingly, apart from inconsistencies with respect to the starting hand, there are further differences between published reports on the finger level, in particular regarding which finger corresponds to the number 6. These will be reviewed next. How finger counting varies: finger-based effects Sato and Lalain (2008) reported that all but three of their participants (all in the age group 4–5 years old, total
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n = 117) showed a symmetry-based finger-digit mapping with the thumb as finger number 6 (symmetrically to the other thumb as number one). In contrast, the study of Lindemann et al. (2011) found that about 32 % of their Western participants continued counting to number six with the pinkie of their right or left hand instead of the thumb. The observation of Lindemann et al. (2011) is inconsistent with the thumb representing the general starting point of the counting procedure independent of starting or transition hand. It does, however, reflect a spatial continuity in the finger-counting process, assuming both hands are held with their palms up with the pinkies of the left and right hand next to each other.
Ad (2) the influence of proprioception: it seems plausible that participants completed the questionnaire by using their dominant hand to write or click (paper–pencil questionnaire or online study), which was the right hand in the majority of cases. In turn, this may have led to a more frequent use of the freely available left hand when starting to count, despite the explicit instruction to hold both empty hands up when counting in the studies of Fischer (2008) and Lindemann et al. (2011). If we apply above model of Fischer and Brugger (2011) to the case of finger counting, such situated cognition factors (here visual perception and proprioception) should influence the embodied cognition on finger counting.
What are possible situated cognition factors in finger-counting assessment?
The current study
Following above idea of situated cognition—as a possible influencing factor of the characteristics of the assessment of finger counting on observed finger-counting habits—a closer inspection of the assessment procedures employed in recent studies may be informative. Indeed, there are significant differences in the assessment of finger-counting habits between those studies. The study of Sato and Lalain (2008) had a more natural setting, where participants were asked to count spontaneously from one to ten with their fingers and were observed while doing so. Consequently they counted freely and no obvious influencing situated factor was present while doing so. Instead, the results of Fischer (2008) and Lindemann et al. (2011) were mainly based on questionnaire data. With having the questionnaire data, there were two main factors that might be situated influencing factors: (1) visual perception, e.g., reading text and visual input from the instruction (e.g., left-to-right arrangement of fingers in the questionnaire) and (2) proprioception that can be described as the sense of the body and its parts, i.e., for our study, the sense for postures and locations. Ad (1) the visual perception: In the questionnaire-studies (Fischer 2008; Lindemann et al. 2011), the instruction was to ‘‘hold your empty hands in front of you and then count aloud from one to ten, using your fingers as you count’’. (see Lindemann et al. 2011). In line with the data reported by Riello and Rusconi (2011), one may argue that, due to the horizontal (left-to-right) perceptual arrangement of fingers of the displayed hands being held palms up (see Fig. 1 Panel b), counting more frequently started on the hand for which mental number line direction and fingercounting sequence matched (i.e., the left hand). Additionally, participants had to read the instruction prior to filling out the questionnaire, so that a left-to-right scheme might have been pre-activated even before participants started to count on their fingers (cf. Shaki and Fischer 2008).
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Based on above model assumption, the aim of the current study was straightforward. We wanted to explore the impact of situated cognition on finger counting by systematically manipulating influence of (1) visual perception (visual input through the horizontal (left-to-right) perceptual arrangement of displayed fingers and instruction) and the influence of (2) proprioception (e.g., writing with a pen before counting) in three different conditions: For a first group of participants, there was no or little situated influence. Participants were just asked to count spontaneously with their fingers, with the finger-counting sequence being watched and noted by the experimenter (corresponding to Sato and Lalain 2008). The second group had only visual perception influence by giving the instruction from the questionnaire orally but with having a horizontal (left-toright) perceptual arrangement of fingers. The instruction for this group was given orally to avoid possible influences of proprioception. For the third group, comparable to Fischer (2008), we synced influence of visual perception and proprioception by using a written instruction in a questionnaire, in which participants had to write down their finger-counting sequence. Prior to the counting, they had to use their dominant hand to fill in the questionnaire. We expected that of those participants who were just asked to count spontaneously and had no intentional influence from situated cognition, most should start counting with their (dominant) right hand (as in Sato and Lalain 2008). In the intermediate group with having just one influencing situated factor (visual perception), we hypothesized that they are less likely to start counting with their (dominant) right hand because of the horizontal (leftto-right) perceptual arrangement of fingers. It is assumed that this left-to-right arrangement leads to the report of more left-starters than in the spontaneous counting group. Further, we expected that participants who had situated influence from (1) proprioception (e.g., writing with a pen prior to counting) and (2) visual perception (e.g., instruction
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a
b
Fig. 1 Experimental setting and instruction in the three participant groups. a Depicts the three participant groups (spontaneous counting condition, perceptual condition, perceptual and proprioception
condition). b Shows the instruction of the questionnaire from group 3 that got the instruction in a written way and used their dominant hand prior to the counting
and displayed hands) should start counting mostly with their left hand (comparable to Fischer 2008). In this case, there is not only influence from the horizontal (left-to-
right) perceptual arrangement of fingers but also the use of the dominant hand prior to counting that is assumed to have a further influence on the report of finger counting. For left-
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starters, we hypothesized that there are the fewest in the first spontaneous counting group but more in the second group with influence from visual perception and most in the group with influences from visual perception and proprioception. Regarding the transition to the second hand (from 5 to 6), we expect that groups also differ in their shown preferences to continue counting with the second hand. Corresponding to Sato and Lalain (2008), we expected that almost all of participants from the spontaneous counting group should proceed with their thumb. Having activated a left-to-rightscheme, we hypothesized that in the group of participants that experienced influence from visual perception more participants should continue counting with their pinkie compared to the spontaneous counting group. In the group with influence from visual perception and proprioception, we expected that similar to Lindemann et al. (2011) that a certain amount of people, more than in the other two conditions, should do the transition to the second hand with using their pinkie.
Methods Participants 458 German participants (237 female, 52 %) took part in the study. Mean age for all groups was 24.70 years (SD = 8.99 years; range: 16.08–79.25 years). Differentiated by each group, mean age was 37.84 (SD = 16.74) years for the spontaneous counting group, 23.73 years (SD = 3.12 years) for the second group with influence from visual perception and 24.27 years (SD = 3.98 years) for the third group with influence from visual perception and proprioception. Age differed significantly between groups (F (2) = 108.40, p \ .001). Participants were either undergraduate students or random passersby that were naı¨ve to the intention of the study. The random passersby were chosen because we wished to examine natural spontaneous counting habits of naı¨ve participants in a situation as natural as possible (i.e., not in an experimental room of the psychological department). For the other conditions, in which situated cognition was manipulated anyway by perceptual or proprioceptive factors, the situation in which counting habits were assessed, was not natural anyway, therefore, these conditions were administered at university. For this reason, random passersby from the spontaneous counting group were standing, while participants from the other two groups were sitting. The majority of participants (95 %) of had Abitur, a general qualification for university.
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Procedure We assigned participants to three groups by means of the experimental setting given: the two questionnaire groups with situated influencing factors were tested in different university courses, whereas for the spontaneous counting group random pedestrians were asked to participate. For a detailed description of groups, see Fig. 1 Panel a. The spontaneous counting group was asked to count spontaneously. Participants had to have both hands freely available and were then asked to count to ten with their fingers. Finger-counting habits were watched and noted by the experimenter (see Fig. 1 Panel a, top chart). The instruction differed slightly from that of the questionnaire conditions by saying: ‘‘Could you please count with your fingers from 1 to 10’’. Prior to the finger-counting assessment, participants performed some finger-hand pantomime activities to assess their handedness (spreading butter, dealing cards, lighting a match). Due to these pantomime activities, participants activated both hands prior to counting and not just mainly one hand (like in the proprioceptive condition, where participants had written with one hand before). After activating both hands, it was assured that participants had both hands freely available, so that there was no proprioceptive bias for natural counting. In the second group with influence from visual perception (see Fig. 1 Panel a, central chart), the instruction was: ‘‘Please hold your empty hands in front of you and then count aloud from one to five, using your fingers as you count’’. Influence of visual perception was due to the spatial left-to-right arrangement of fingers in the questionnaire (see Fig. 1 Panel a, central chart). This instruction was given orally, so that they had both hands available prior to the counting and no influence from proprioception. Participants were asked to count to ten with their fingers and then fill in the finger counting as well as demographic and handedness questionnaire after counting was completed. In line with the procedure of previous studies (Fischer 2008; Lindemann et al. 2011), the third group with influences from visual perception and proprioception received a written instruction with a customized print-out version of the online questionnaire from Lindemann et al. (2011), (see http://fingercounting.cognitive-psychology.eu/hcq_ paper_supplementary/). Prior to the finger-counting task (see Fig. 1, Panel a, lower chart), a demographic and handedness questionnaire had to be completed. This means that they used their dominant hand prior to finger counting (influence of proprioception) and were influenced by the spatial arrangement of fingers. The hand posture in this group was predefined by the form of instruction: palm-up, next to each other.
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Of the 458 included participants, 68 (50 % female, 93 % right-handed) were asked to count spontaneously, 252 (44 % female, 90 % right-handed) were in the second group with influence from visual perception and 138 (68 % female, 90 % right-handed) were in the third group with influence from visual perception and proprioception. Handedness About 91 % of the sample was right-handed (n = 415), 7 %, left-handed (n = 29) and 3 %, bilateral (n = 14). Of these 29 left-handers, 24 (83 %) started counting with their dominant hand, whereas there was no such tendency in right-handers for whom starting hand was balanced (50 % right-starters). In the spontaneous counting group, three activities were monitored as participants were instructed to pantomime them prior to the counting: (1) to hand out playing cards, (2) to spread butter on bread and (3) to light a match. Additionally, participants were asked about their handedness to confirm the handedness-activity judgment. In the two groups with influence from situated cognition, handedness was assessed with 13 items (e.g., Which hand do you use for… writing?), similar to the study by Fischer (2008).
Results When there were directed empirical hypotheses, these hypotheses were statistically tested in a directed way (e.g., one sided) whether possible to match empirical and statistical hypotheses as closely as possible, because overall statistics can be too conservative and thus misleading (e.g., Hager 2002). All but one participant used the fingers of both hands to count from one to ten; so, they started with either their left or right hand for the first five numbers and continued counting with the other hand for numbers six to ten. The person who counted with only one hand used the right hand and was in the third group with influence from visual perception and proprioception. Hand-based results Results showed that participant groups differed systematically with respect to the hand with that counting was started [v2(2) = 21.89, p \ .001]. When participants counted spontaneously with no influence of situated cognition, only about 28 % started with their left hand. In the second group with influence from visual perception, preference was approximately balanced with 54 % left-starters. Contrarily, in the third group with influences from visual
Fig. 2 Percentage distribution of right- and left-starters in the three different instruction conditions. Note that in the spontaneous counting group most participants started with their right hand, whereas the more situated influences the more participants started with their left hand
perception and proprioception, about 62 % started counting with their left hand (see Fig. 2). More specific testing revealed that the reversal from 72 % right-starters in the spontaneous counting group to 62 % leftstarters in the group with influences from visual perception and proprioception was significant [v2(1) = 21.54, p \ .001]. Additionally, the shift from 28 % left-starters in the spontaneous counting group to 54 % left-starters in second group with influences from visual perception was significant [v2(1) = 14.09, p \ .001]. Finally, the difference between the two groups that were influenced by situated cognition was also significant [v2(1) = 2.78, p \ .05]. Finger-based results Almost all participants (98 %) started counting with either one of their thumbs. However, the transition to the second hand (finger number 6) differed significantly between groups [v2(6) = 46.75, p \ .001]. As illustrated in Fig. 3, all participants (100 %) in the spontaneous counting group with both hands available continued counting on their second hand with their right/left thumb. In the group with influence from visual perception, 13 % continued with their right pinkie (6 % left pinkie), and 26 % of the participants that were influenced by visual perception and proprioception continued with their right pinkie (4 % left pinkie). Additional testing indicated that the finger used to count number six differed significantly for all pairwise comparisons between the three instruction groups [all v2(3) [ 10.80, all p \ .013]. Possible gender differences There were unexpected gender differences between the instruction groups. In the spontaneous counting group with
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Fig. 3 Percentage distribution of fingers corresponding to the number six separated for the three different instruction conditions. Note that no one in the spontaneous counting group continued with their pinkie, whereas in the other two questionnaire groups with influence of situated factors a considerable part (20–30 %) of the participants did. This pattern is related to a spatial congruent counting pattern. Again this pattern was most pronounced in the group with visual perception and proprioception
both hands freely available (50 % female participants), no gender differences were found. Differences between male and female participants were observed in second group with influences from visual perception (44 % female participants) with respect to the finger associated with number six. This was mainly because women continued counting with their right pinkie about as often as with their left pinkie (10 %, respectively, 11 %), whereas men tended to count on more likely with their right pinkie (15 %) and only rarely with their left pinkie (2 %) when they continued with their pinkie. In the third group with influences from visual perception and proprioception (68 % female participants), differences were observed for the finger associated with number one and number six. Results showed that women were particularly more likely to start with their left hand in the instruction group, whereas starting hand was almost balanced in men.
Discussion Finger-counting habits are influenced by situated cognition: Hand-based effects Based on the model of Fischer and Brugger (2011; see also Fischer 2012), we hypothesized that besides grounded and embodied aspects, finger-counting habits are also influenced by situated aspects. Therefore, we assessed the finger-counting patterns of three different groups and varied the amount of situated influences: (1) spontaneous counting with both hands available (as in Sato and Lalain 2008), (2) visual perception: counting with horizontal (left-to-right) perceptual arrangement of fingers (3) visual perception and proprioception:
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counting with horizontal (left-to-right) perceptual arrangement of fingers and with busy dominant hand prior to counting (as in Fischer 2008). Participants in the spontaneous counting group had no or just little influence of situated cognition as the setting was natural and the instruction did not pre-activate a specific spatial representation. Congruent to other studies, we expected most participants to start with the (dominant) right hand (Di Luca et al. 2006; Sato and Lalain 2008). In the perceptual condition, participants were tested with a questionnaire that showed a horizontal left-to-right arrangement of fingers. We hypothesized that due to the visual perception of the finger arrangement, participants should count differently compared to spontaneous counting with more left-starters because of the given horizontal (left-to-right) arrangement in the German left-to-right reading culture. In the perceptual and proprioceptive condition, participants not only were influenced by the horizontal (left-to-right) perceptual arrangement of fingers but also used their dominant (right) hand for writing and holding a pen prior to the counting (proprioception). Therefore, there were two situated factors that—according to our extension of the Fischer and Brugger (2011) model— should influence participants even stronger than the group with only visual perception; so, we expected that the majority would be left-starters similar as it was in Fischer (2008) and Lindemann et al. (2011). In line with these hypotheses, the current results indicate that finger-counting patterns indeed differed depending on situational factors at the time of data collection. Depending on condition, we observed reliable differences between participant groups regarding the starting hand (right or left): In the spontaneous counting group with no or little influence of situated factors, only 28 % of participants were left-starters. In the second condition, in which visual perception (left-to-right alignment of hands/finger) was present, significantly more participants started with the left hand (54 %). Finally, in the group with perceptual and proprioceptive influences, even more participants (62 %) started to count with their left hand. These data show that the proportion of left- and right-starters almost reversed (72 % right-starters in condition 1, but 62 % left-starters in condition 3) and thus showed a pronounced impact of the situational manipulation. In our view, this is strong evidence that not only grounded factors based on universal physical laws of the world, and embodied factors, based on culturally mediated sensori-motor learning directions (e.g., reading direction), but also situated factors strongly influences participants’ report of their finger-counting habits. The situated cognition account reconciles apparently inconsistent findings in the literature Such a situated cognition account of finger-counting habits is not only theoretically interesting for the validity of the
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Fischer and Brugger (2011) model for finger counting. Rather, this account has also important practical implication because it reconciles apparently inconsistent results in the literature: For our questionnaire instruction groups with influences from situated factors, we used the same questionnaire as Fischer (2008) and Lindemann et al. (2011) and observed congruent results with about two-thirds of participants being left-starters. In contrast, in the spontaneous counting group with both hands freely available, we replicated the experimental setting of Sato and Lalain (2008) and obtained similar results with about three quarters of participants starting with their right hand. Thus, we can assume that the stronger situational influences of perceptual or proprioceptive aspects favoring a left hand start of finger counting in a left-to-right reading culture, the greater is the proportion of left-starters. In the group with two influencing situated factors, most participants started with their left hand, in the group with one influencing factor about half of the participants started with their left hand and in the spontaneous counting group with no or only little situated influence an minority started with the left hand. While our study provides evidence that the examination situation influences responses, we also wish to acknowledge that there may be other situated factors, which may influence responses differentially in different experiments and may contribute to of finger-counting habits being modulated by situational factors. For instance, we tried to realize a natural setting in the spontaneous counting group similar to Sato and Lalain (2008) and examined participants even outside formal experimental laboratories to obtain a finger-counting report as natural and as naı¨ve as possible. On the other hand, we used questionnaire conditions as in Fischer (2008) or Lindemann et al. (2011) for which people have to fill out a questionnaire form prior to counting. Despite the visual-perceptive and proprioceptive manipulations we examined, these led to some other situated influences regarding experimental group (students vs. random passersby) and differences in body position (sitting vs. standing) in the spontaneous counting versus the other two groups. Additionally, it is conceivable that even within the spontaneous counting group who had both hands freely available and activated before counting, spontaneous hand or finger postures (e.g., palm-up, palm-down, cf. Riello and Rusconi 2011) prior to counting may also lead to situated influences, which influence counting habits. The demonstration of some situated cognition aspects strongly influencing finger counting does not preclude that other associated or not manipulated situated aspects can also influence finger-counting habits in this and other studies. Given that the situated manipulations revealed rather large effects in our study, further investigation of situated fingercounting factors seems worthwhile in our view.
Finger-counting habits are influenced by situated cognition: finger-based effects Further evidence that situated cognition had an important influence on the number-to-finger mapping came from the results regarding the finger associated with the number six. All participants in the spontaneous counting group continued counting with their thumb when transferring from 5 to 6. This was different in the other two conditions: About 20 % (perceptual condition) and 30 % (perceptual and proprioceptive condition), respectively, used their pinkie to indicate finger number six. So, one can assume that situated factors led to a specific hand position that activated a spatially continuous representation in 20–30 % of the participants in the questionnaire instruction groups with influencing situated factors. This pattern was again significantly stronger for influences from perception and proprioception compared to the influence of perception only. According to our theoretical account that the situated influence triggered a left-to-right-scheme, most of the participants with a spatially continuous pattern counted in a way replicating a left-to-right oriented number line where—when looking at hands palm-up—there is a continuous transition from the left to the right pinkie. We assume that the situated influence from the horizontal (leftto-right) perceptual arrangement of fingers as well as the prior use of the dominant (right) hand corroborated the activation of such a mental number line representation from left-to-right. This is in line with the results of Riello and Rusconi (2011) who found that a palm-up posture of the left hand facilitates a systematic left-to-right oriented mental number line representation. An extension and specification of the Fischer and Brugger (2011) model to finger-counting habits Generally, these results fit to the model of grounded, embodied and situated cognition (Fischer and Brugger 2011; Fischer 2012). According to the model grounded cognition can be described as universal features that apply to physical laws, e.g., that larger numerosities are more and include smaller numerosities. Embodied cognition is defined as sensori-motor (embodied) knowledge representation that is acquired during typical learning and is formed by culture, while situated cognition can be seen as the influence of situation and context that affects different results due to different situations a person is examined in. Within SNAs, grounded, embodied and situated cognition seem to be well established as described in the introduction. These results for SNAs will be shortly summarized here before generalizing these results to finger counting: (1) The influence of grounded cognition can be found in results that show the universal association
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between smaller numbers and lower space, respectively, between larger numbers and upper space (Fischer 2012; Shaki and Fischer 2012). (2) Influence on embodied cognition can be found in the study from Shaki et al. (2009) that show that different cultures differ in the direction of the SNARC effect. (3) Influences of situated cognition on SNAs can be found in different studies, e.g., Fischer et al. (2009): Bilingual participants saw randomly from trial to trial either a Russian (left-to-right) or a Hebrew (right-toleft) word. The SNARC effect in these participants was only present when they read the Russian left-to-right word. We adapted this model from Fischer and Brugger (2011) and Fischer (2012) to specifically incorporate finger counting (see Fig. 4). When looking at finger-counting habits, studies regarding grounded and embodied cognition only have been reported so far (e.g., Di Luca et al. 2010; Lindemann et al. 2011, see introduction). Within finger counting, grounded cognition means that a larger numerosity of fingers represent a larger number and (at least for the Western counting system) includes smaller numerosities. This is in line with the results of Di Luca et al. (2010) regarding place versus summation coding in a priming task. Cultural differences measured with the same questionnaire indicate influences of embodied cognition (Lindemann et al. 2011). However, from our point of view, there was a gap regarding the influence of situated cognition in finger counting. With the present study, we tried to close this gap by showing the influence of situated cognition on natural finger-counting habits. In the present study, these situational factors can be described as visual perception and proprioception (see Fig. 4). From the current results, we conclude that there are
Situated cognition Influence of testing-situation e.g., left-to-right arrangement of fingers and one hand busy holding pencil visual perception
Present study
proprioception
Embodied cognition Typical body postures/ typical spatial reference frame related to culture or typical learning (e.g., reading direction)
Grounded cognition Larger numerosities are more e.g., more fingers represent larger numbers
e.g., Lindemann et al. (2011)
e.g., Di Luca et al. (2010)
Fig. 4 Extension and specification of the Fischer and Brugger (2011) model to finger-counting habits. Influences of grounded, embodied and situated cognition on finger counting are displayed. The present study examines influencing factors from situated cognition
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indeed influences of situated factors that modulate participants finger-counting habits (even within the same culture). Interestingly, the results of our study show not only an influence of situated cognition but results also indicate that the power of this situated influence can be varied. The more influencing situated factors favored left-to-right counting habits the more participants tended to be leftstarters: From 28 % left-starters in the spontaneous condition, proportion of left-starters rose to 54 % with one influencing situational component favoring left-starting in our culture (visual perception of the left-to-right arrangement of fingers) and further on to 62 % with two components of situated influence (visual perception and proprioception). In the finger-counting model (see Fig. 4), this aspect is indicated by different pathways from situated to embodied cognition. Note that these pathways also indicate that the influence of situated factors may differ depending on the embodied representation it addresses. For instance, in right-to-left-reading cultures horizontal alignment of fingers may activate right-to-left SNAs (e.g., Shaki et al. 2009) and therefore lead to more right-hand starters rather than to more left-starters as in the current study.
Conclusions and perspectives Based on the present data and their theoretical implementation, we suggest that finger counting (in Western cultures) is stereotypical in certain ways, as participants almost always started with either one of their thumbs. However, the use of the right or left hand seems to be highly susceptible to the influence of situated factors. When people count on their fingers spontaneously and have both hands available, they seem to prefer to start finger counting with their dominant (right) hand. This result is in line with Previtali et al. (2011) who suggest that starting hand preference mainly derive from handedness preferences. Visual perception of a left-to-right arrangement of fingers and the proprioception of holding a pen in the dominant (right) hand prior to counting might increased the influence of a mental left-to-right-scheme, so that increasingly more participants started to count with their left hand. Extending the notion of the embodiment of cognitive processes, in which the spontaneous typical finger-counting habit is seen as an instance of embodied cognition (Domahs et al. 2010; Fischer and Brugger 2011; see Barsalou 2008 and Wilson 2002 for an overview of embodied cognition), we argue that counting patterns are influenced by situated cognition. This is in line with the idea of situated cognition to depend on task-relevant inputs and outputs (Wilson 2002; Robbins and Aydede 2009). A tentative explanation for the observed gender differences might be that different spatial schemes are activated
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in men or women due to the influence of visual perception and proprioception. One might suspect that women are more influenced by the spatial orientation of their hands. The influence of situated cognition could have lead to a faster activation of the left-to-right-scheme, so that therefore women are more likely left-starters. However, at this point this remains speculative and needs to be investigated systematically in future studies evaluating what underlying processes may contribute to the observed differences in counting patterns between men and women. Taken together, we argue that finger counting is influenced by grounded, embodied and situated cognition (see Fig. 4). In this study, we examined the influence of situated cognition, in particular, visual perception and proprioception. By simply manipulating the amount of situated cognition, we could observe significant differences in counting patterns within the same culture. We conclude that when counting spontaneously, handedness preference determines starting hand, but when left-to-right schemes are pre-activated due to situated factors a shift to increasingly more left-starters and a more spatial congruent transition to the second hand can be observed. This corroborates the relevance of situated cognition because even a highly overlearnt practice such as finger counting depends strongly on its situational constraints. We suggest that the situational constraints in our study as well as other possible situational aspects should be further studied to obtain a better picture on the situated cognition influences on finger counting. Acknowledgments Mirjam Wasner, Korbinian Moeller and HansChristoph Nuerk are members of the ‘‘Cooperative Research Training Group’’ of the University of Education, Ludwigsburg and the University of Tuebingen, which is supported by the Ministry of Science, Research and the Arts in Baden-Wu¨rttemberg. They are also associated with the LEAD Graduate School of the University of Tuebingen, which is funded within the framework of the Excellence Initiative via the German Research Foundation. Martin H. Fischer was supported through DFG Grant FI 1915/2-1 on ‘‘Manumerical cognition’’.
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